The explosion took place at Imam Sadiq Mosque in Kuwait City, BBC reported. The Islamic State group claimed the responsibility for the deadly attack.
The IS-affiliated group in Saudi Arabia, calling itself Najd Province, said militant Abu Suleiman al-Muwahhid carried out the attack on the mosque, which it claimed was spreading Shiite teachings among Sunni Muslims.
ISIS, a radical Sunni Muslim group, considers Shiites to be heretics.
Medics said the suicide bombing killed "at least 13 people, while 25 others were hospitalised."
Najd Province claimed similar bombings against Shiite mosques in Saudi Arabia in recent weeks.